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Questions and Answers

Match the components of decision analysis with their descriptions:

Decision Alternatives = Different courses of action available to a decision maker States of Nature = Uncertain future events that affect the outcome Payoffs = Consequences associated with decision alternatives Problem Formulation = The initial step in decision analysis outlining the problem

Match the terms used in decision analysis with their definitions:

Decision Alternatives = Options among which choices are made States of Nature = Possible scenarios that can occur Payoffs = Results or outcomes from selected options Combinations = Pairs formed from decision alternatives and states of nature

Match the elements of a decision problem with their roles:

Decision Alternatives = Represent strategies or choices States of Nature = Serve as variables in uncertain environments Payoffs = Indicate the results of decisions Problem Formulation = Establishes the framework of the decision issue

Match the types of analysis used in problem formulation with their purposes:

Probabilities = Assess likelihood of different states of nature Sample Information = Utilize past evidence to inform decisions Bayes’ Theorem = Calculate conditional probabilities Decision Making = Choosing the best alternatives based on analysis Signup and view all the answers

Match the chapters and concepts in 'Statistics for Business and Economics' with their focus areas:

Chapter 21 = Decision Analysis Problem Formulation = Defining the problem clearly Decision Making with Probabilities = Incorporating chance into decisions Computing Branch Probabilities = Using Bayes’ Theorem for calculations Signup and view all the answers

Match the following terms related to decision making with their definitions:

Decision Alternatives = Possible strategies a decision maker can employ States of Nature = Future events not controlled by the decision maker Mutually Exclusive = Events that cannot occur simultaneously Collectively Exhaustive = All possible events accounted for Signup and view all the answers

Match the following concepts with their descriptions in decision making:

Payoff = Consequence of a decision alternative and a state of nature Contingency Planning = Planning for unexpected states of nature Risk = Potential for loss associated with states of nature Decision Matrix = Framework for evaluating decision alternatives and outcomes Signup and view all the answers

Match the following aspects of decision making with their characteristics:

Decision Maker = Individual or group making choices Outcome = Result of the chosen decision alternative Analysis = Process of evaluating potential states of nature Scenario = Specific set of conditions affecting decision making Signup and view all the answers

Match the following decision-making terms with their examples:

Decision Alternative = Selecting a marketing strategy State of Nature = Market trends affecting consumer behavior Payoff Table = Chart listing outcomes for each combination of decisions and states Expectation = Probability-weighted average of payoffs Signup and view all the answers

Match the following strategies with their related concepts:

Maximax = Maximizing the maximum possible payoff Maximin = Maximizing the minimum possible payoff Minimax Regret = Minimizing potential regret for misjudgment Optimistic Approach = Assuming best-case scenarios in decision making Signup and view all the answers

Study Notes

Statistics for Business and Economics (13e)

Authored by Anderson, Sweeney, Williams, Camm, Cochran
Published by Cengage Learning in 2017
Slides by John Loucks, St. Edwards University
Includes modifications by Reid Kerr

Chapter 21: Decision Analysis

Topics include Problem Formulation, Decision Making with Probabilities, Decision Analysis with Sample Information, and Computing Branch Probabilities using Bayes' Theorem

Problem Formulation

The first step in decision analysis involves defining the problem verbally.
Decision alternatives, states of nature (uncertain future events), and payoffs (outcomes) must be identified.
A specific combination leads to a payoff.
Payoffs can be in terms of profit, cost, time, distance, or any other measurement.
States of nature should be mutually exclusive and collectively exhaustive.
A decision problem is characterized by decision alternatives, states of nature, and resulting payoffs.
The decision alternatives are the possible strategies a decision-maker may employ.
States of nature refer to future events beyond the control of the decision-maker.
States of nature must be mutually exclusive and collectively exhaustive.

Payoff Tables

The consequence, resulting from a specific combination of decision alternative and state of nature, is a payoff.
A payoff table shows all possible combinations of decision alternatives and states of nature with associated payoffs.
Payoffs can be expressed in various ways, including profit, cost, time, distance, or other relevant measurements.

Table 21.1

Payoff table for PDC condominium project
Payoffs are in millions of dollars
Shows payoffs for three possible scenarios (30, 60, 90 condominiums) and two states of nature: strong demand and weak demand

Decision Trees

A graphical representation showing the sequential nature of the decision-making process.
Two types of nodes:
- Round nodes represent states of nature
- Square nodes represent decision alternatives.
Branches from round nodes indicate the various states of nature.
Branches from square nodes represent various decision alternatives.
Payoffs are at the end of each branch.

Decision Making with Probabilities

After defining decision alternatives and states of nature, probabilities must be determined, often using the frequency method or a subjective method.
Probabilities must satisfy two conditions:
- P(s) ≥ 0 for all states of nature
- Σ P(s) = 1, where N represents all possible states of nature

Decision Making Under "Uncertainty"

Maximin: Choose alternative that maximizes the minimum possible payoff (pessimistic).
Maximax: Choose alternative that maximizes the maximum possible payoff (optimistic).
Expected Monetary Value (EMV): Using prior probabilities for states of nature, calculate the expected payoff for each alternative. Select the alternative with the largest EMV.

Expected Value Approach

The expected value of a decision alternative is the sum of the weighted payoffs.
The expected value (EV) of decision alternative d is defined as EV(d) = Σ P(s)V(d, s) , where N is the number of states of nature, P(s) is the probability of state s, and V(d, s) is the payoff corresponding to decision alternative d and state s.

Expected Value of Perfect Information (EVPI)

The increase in expected profit if the state of nature is known with certainty.
Provides an upper bound on the expected value of any sample or survey information.

Computing Branch Probabilities Using Bayes' Theorem

Bayes' Theorem can be used to determine branch probabilities in decision trees.
Prior probabilities are initial probabilities for states of nature.
Conditional probabilities are probabilities of outcomes given a state of nature.

Expected Value of Sample Information

The additional expected profit possible from knowledge of the sample or survey information (EVSI).
Calculated by subtracting the expected value without sample information (EVwoSI) from the expected value with sample information (EVwSI).
Determines the value of acquiring more information.